Question: The following line passes through point $(9, -3)$ : $y = -\dfrac{13}{18} x + b$ What is the value of the $y$ -intercept $b$ ?
Answer: Substituting $(9, -3)$ into the equation gives: $-3 = -\dfrac{13}{18} \cdot 9 + b$ $-3 = -\dfrac{13}{2} + b$ $b = -3 + \dfrac{13}{2}$ $b = \dfrac{7}{2}$ Plugging in $\dfrac{7}{2}$ for $b$, we get $y = -\dfrac{13}{18} x + \dfrac{7}{2}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(9, -3)$